Kinetics of absorption of water by filled epoxide polymers

The kinetics of the absorption of water by composite materials based on an epoxide binder and glass microspheres were investigated. It was shown that the absorption of water by these materials has the character of a stage mechanism due to destruction of the adhesion between the binder and the microspheres. Treatment of the glass spheres with a coupling agent not only reduces the water absorption but also changes the character of the kinetic curve for water absorption. It was shown that a thermomechanical method can be used to evaluate the stability of the adhesion bonds between the polymer and the filler under the influence of water.Vladimir Scientific-Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, No. 2, pp. 290–294, March–April, 1972.     

Nonnegative matrices with zero permanent

We studym×n matrices,mn, whose elements are either 1) arbitrary nonnegative numbers or 2) belong to a given finite set of nonnegative numbers that includes zero. In the finite case, we obtain an asymptotic expression, asn , for the number of matrices with zero permanent. For any nonnegative matrix with zero permanent a standard representation is derived.Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 493–504, October, 1995.This work was partially supported by the Russian Foundation for Basic Research under grant No. 93-011-1443.     

Estimates of the independence number of a hypergraph and the Ryser conjecture

For the Legendre-Sobolev orthonormal polynomials depending on the parametersM≥0,N≥0, weighted and uniform estimates on the orthogonality interval are obtained. It is shown that, unlike the Legendre orthonormal polynomials, the polynomials forM>0,N>0 decay at the rate ofn ^−3/2 at the points 1 and −1. The values of are calculated. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 871–880, December, 1997. Translated by N. K. Kulman     

Partially decomposable and totally indecomposable nonnegative matrices

We considerm×n (mn) matrices with entries from an arbitrary given finite set of nonnegative real numbers, including zero. In particular, (0, 1)-matrices are studied. On the basis of the classification of such matrices by type and of the general formula for the number of matrices of nullityt valid fort>n andtn>m (see [2]), an asymptotic (asn ) expansion is obtained for the total number of: (a) totally indecomposable matrices (Theorems 1 and 5), (b) partially decomposable matrices of given nullitytn (Theorems 2 and 4), (c) matrices with zero permanent (without using the inclusion-exclusion principle; Corollary of Theorem 2).Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 643–662, May, 1996.The work of the second author was supported by the Russian Foundation for Basic Research under grant No. 93-011-1443.